Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 855 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
3. 3.A cube has edges of 11 cm. What is its total surface area? (a) 121 sq cm (b) 1331 sq cm (c) 726 sq cm (d) 484 sq cm
4. 4.A cube has edges of 8 cm. What is its volume? (a) 24 cu cm (b) 256 cu cm (c) 384 cu cm (d) 512 cu cm
5. 5.A cuboid is 4 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 84 sq cm (b) 122 sq cm (c) 61 sq cm (d) 244 sq cm
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
7. 7.A cuboid is 5 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 40 cu cm (b) 11 cu cm (c) 76 cu cm (d) 10 cu cm
8. 8.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 1728 cu cm (c) 36 cu cm (d) 576 cu cm
9. 9.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
10. 10.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
11. 11.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
12. 12.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
13. 13.A cuboid is 6 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 236 sq cm (b) 240 sq cm (c) 118 sq cm (d) 472 sq cm
14. 14.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
15. 15.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
16. 16.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
17. 17.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 176 sq cm (b) 48 sq cm (c) 88 sq cm (d) 44 sq cm
18. 18.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
19. 19.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 49 sq cm (c) 196 sq cm (d) 343 sq cm
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
21. 21.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
22. 22.A cuboid is 6 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 49 cu cm (b) 12 cu cm (c) 88 cu cm (d) 48 cu cm
23. 23.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
24. 24.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
25. 25.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
26. 26.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
27. 27.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
28. 28.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 27 cu cm (c) 486 cu cm (d) 324 cu cm
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
30. 30.A cube has edges of 12 cm. What is its total surface area? (a) 144 sq cm (b) 1728 sq cm (c) 864 sq cm (d) 576 sq cm
31. 31.A cuboid is 7 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 15 cu cm (b) 28 cu cm (c) 144 cu cm (d) 112 cu cm
32. 32.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 24 sq cm (c) 16 sq cm (d) 8 sq cm
33. 33.A cuboid is 6 cm long, 5 cm wide and 4 cm high. What is its volume? (a) 148 cu cm (b) 30 cu cm (c) 15 cu cm (d) 120 cu cm
34. 34.A cuboid is 11 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 430 sq cm (b) 215 sq cm (c) 550 sq cm (d) 860 sq cm
35. 35.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
36. 36.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
37. 37.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
38. 38.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
39. 39.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
40. 40.A cuboid is 11 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 89 sq cm (b) 178 sq cm (c) 132 sq cm (d) 356 sq cm

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